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Remarks at the panel discussion on “d-wave superconductivity”
J. Phw. Printed
Chrm in Great
Solids Vol. Britain
54.
No
IO.
pp
1457-1459.
C022-3697193 $6 00 + 0.00 Pergamon Press Ltd
1993
Remarks at the Panel Discussion on “d-Wave Superconductivity” P.W. ANDERSON* Joseph Henry Labomtotics of Physics Jadwin Hall. Princeton University Princcton. NJ 08544
* Panel Discussion, Conference on Spectroscopies in Novel Superconductors, sponsored by LANL, March 17-19, Santa Fe, NM
The spin fluctuation “theory” of high Tc superconductivity does not seem to me to have any of the characteristics in style or substance of a successful theory. If we look back on explanations of the phenomena of condensed matter physics which have been successful in the past, such as the Debye theory of specific heats, the Pauli theory of metals, the BCS theory of superconductivity, the Kondo theory, the theory of 3He, and several others, we find a common style for each. I would characterize this style by conceptual depth combined with, at least at first, considerable compu~tional simplicity and, above all, by a bunt ability to cope with ditative anomalies which had arisen in experiments. Such anomalies were the T3 low T specific heat for phonons, the constant susceptibility and linear T specific heat for metals, the range and scale of Tc and the independence from dirt effects for superconductivity, the log T resistivity for magnetic impurities, the contrast in spin susceptibility between two phases of the same Tc (and the co-existence of these phases) for 3C;re. Each of the examples mentioned, and in fact essentially all the breakthrough solutions of condensed matter problems I know of, had in common that they (a) disposed of many of the q~i~tive anomalies almost at a glance; (b) involved new, deeper concept~~ations of the relevant physics. In some of their writings the promulgators of the spin fluctuation theories have actually taken pride in the fact that their approach is the diametrically opposite one of “conceptual simplicity and computational complexity”: that each experimental result is to be laboriously calculated for each individual substance, and that there is essentially no common background of physics, no generic behavior or at least no reason for one. In all of the examples I have given above, the opposite is true: the stage of computation comes much kter than that of conceptualization. There are many exact or quasiexact results which do not depend at all on the detailed physical parameters, such as e.g., the detailed phonon spectrum for Debye’s specific heat or the shape of the Fermi surface in the theory of not unders~d normal metals. If it had been necessary to do them this way, case by case, we would a solids. I have made here essentially 3 points: (a) (b) fc)
Conceptual Depth Qualitative Tests Computational Opacity. PTUAL
DEPTK
Here then are serious problems with the “antiferromagnetic spin fluctuation theory” as proposed initially by Moriya and followed up by Scalapino, Millis and Pines. Antiferromagnetism in most substances in which it occurs is a consequence of their being Mot&Hubbard insulators. The corresponding superexchange theory is a proiective perturbation theory in l/U, which is carried over to the metallic state by the “t - J” ~~sfo~ation.
This is incompatible with a probation
in positive powers of U, since J = i
unless
major resummations are carried out. More important, the projective character of the t - J H~iltonian enforces a local constmint-i.e., an infinite number of conservations-which implies rigorously one Lagrange multiplier for each constraint, i.e., a massless gauge field. That the result can be modeled by simple perturbation theory is a bold, but almost certainly incorrect, conjecture. It does not work in one dimension, the only case we can rigorously solve. I have shown that it does not work in two, but my solution is approximate and only applies in the limit w + 0. 1457
P. W. ANDERSON
1458
IVE TESTS, t The question is whether there are any simple, generic behaviors, and whether they are indicated by this theory. The answers are yes and no.
Let me first dispose of a large class of red herrings. As Mott explained to us in 1949 and 1956, metal insulator transitions are usually discontinuous, and this one is no exception; as beautifully shown by the laser-induced superconductivity experiments among others. (Also by Jim Allen’s photoemission results.) Underdoped materials are pathological: either inhomogeneous or beset with localized defects. It is a pity so much good experimental effort has been wasted on them, especially the neutron work. There are two, essentially, stable metallic phases: fully doped and overdoped metals (often separated by a phase transition, as Takagi and Batlogg showed). The latter is more Fermi liquid-like; the former is the optim~ly doped superconducting phase. These optimally doped phases are remarkably similar in their normal state behavior; e.g, Batlogg has shown that dp&iT at - 100’ does not vary (per plane) by more than - 20% for 4 of them and I have estimated a number of others and found agreement They all show: (a)
Linear T and o resistivity: 9 = max(;)
(b) (c)
&falIOT+ (Mean fme pathlCCCc. (Infrared transparencyEk)
(a)
Linear w Raman background.
The most striking plot is of 9~~7’~
for a wide variety of these materials. The correlation
coefficient is exactly zero with probability unity: normal state properties are m with T,, from material to material, A theory which attempts to explain Tc with the same physics as normal state resistivity, as the spin fluctuations do, must encounter skepticism. (They are not alone, of course: anyons, spin bags, bipolarons, etc., all have the same problem.) There is no natural “back-of-the-envelope” explanation for any of these regularities. A number of other observations are almost equally generic and/or anomalous . The photoemission spectra are the most striking, as explained in my talk at this conference: spin fluctuations do not address these anomalies. The anomalous relaxation (Tl and T2) results in NMR are carefully fitted; but simpler*power law tits from other theories are equally good in the normal state.
0
COMPUTATIONAL OPACITY..
Finally, let me say a few words about computational “opacity” (my synonym for “complexity”). Because of the great popularity of the computer, especially as a training tool to keep the young gainfully, if not usefully, occupied, it has become somehow a sign of virtue for a theoretical investigation to involve heavy use of the computer, either for computation or for simulation. Of course the computer can be useful, but not, I would argue, in the kind of problem-~lving investi~tion necessary to unravel high TC. The minute a cakulation disappears into the computer it has become unch~~b~ and unedible. Physicists have learned that experiments m be independently reproduced before belief sets in, but unfortunately computer work has not been held to the same standard. This is necessary especially in the kind of calculations involved here, where there is a large universe of parameters, no control on the theoretical approximations used, the input experiments have unknown validity and limits of error, and there is no way for a completely independent investigator making independent choices to verify the results. I would argue that a claimed “nparameter fit” to an experimental datum carries little weight. This is true especially when every curve on every substance must be ~de~endy calculated in detail. I do not feel that one is dealing here with deliberate fraud, as may be the case with W. S. Goddard’s calculations, but rather with optimism and self-deception. I do feel that in our misuse of the computer we condensed matter physicists are in danger of opening ourselves to problems of ethics which we have been happily free from in the past.
D-wave superconductivity
1459
I do not want to end on such a finger-pointing tone. High Tc has confronted our community with a set of anomalies which am forcing us to go through a Kuhnian (mini-) revolution in our thinking. We are in the “crisis” stage in which similar past communities have often exhibited irrational behavior. It is not irrational for some to propose impossible conjectures in such a crisis; what is perhaps blameworthy is for the audience to take them seriously without checking them against reality. POSTSCRIPT The import of the above is that the specific shape of the energy gap is not very relevant to the problems of the theory. Nonetheless it is an interesting question. I do not see how either the observation of an isotope effect in many cases or the insensitivity of Tc to massive amounts of dopant impurities can be made compatible with a gap with nodes, unless new physics is involved. My guess is an anisotropic s-wave gap. The data are not inconsistent with that calculated by Chakravarty et al. The claim that the impurity effect has been calculated in s.f. theory is nonsense, since the absence of residual resistance is not explained in that theory.
Chrm in Great
Solids Vol. Britain
54.
No
IO.
pp
1457-1459.
C022-3697193 $6 00 + 0.00 Pergamon Press Ltd
1993
Remarks at the Panel Discussion on “d-Wave Superconductivity” P.W. ANDERSON* Joseph Henry Labomtotics of Physics Jadwin Hall. Princeton University Princcton. NJ 08544
* Panel Discussion, Conference on Spectroscopies in Novel Superconductors, sponsored by LANL, March 17-19, Santa Fe, NM
The spin fluctuation “theory” of high Tc superconductivity does not seem to me to have any of the characteristics in style or substance of a successful theory. If we look back on explanations of the phenomena of condensed matter physics which have been successful in the past, such as the Debye theory of specific heats, the Pauli theory of metals, the BCS theory of superconductivity, the Kondo theory, the theory of 3He, and several others, we find a common style for each. I would characterize this style by conceptual depth combined with, at least at first, considerable compu~tional simplicity and, above all, by a bunt ability to cope with ditative anomalies which had arisen in experiments. Such anomalies were the T3 low T specific heat for phonons, the constant susceptibility and linear T specific heat for metals, the range and scale of Tc and the independence from dirt effects for superconductivity, the log T resistivity for magnetic impurities, the contrast in spin susceptibility between two phases of the same Tc (and the co-existence of these phases) for 3C;re. Each of the examples mentioned, and in fact essentially all the breakthrough solutions of condensed matter problems I know of, had in common that they (a) disposed of many of the q~i~tive anomalies almost at a glance; (b) involved new, deeper concept~~ations of the relevant physics. In some of their writings the promulgators of the spin fluctuation theories have actually taken pride in the fact that their approach is the diametrically opposite one of “conceptual simplicity and computational complexity”: that each experimental result is to be laboriously calculated for each individual substance, and that there is essentially no common background of physics, no generic behavior or at least no reason for one. In all of the examples I have given above, the opposite is true: the stage of computation comes much kter than that of conceptualization. There are many exact or quasiexact results which do not depend at all on the detailed physical parameters, such as e.g., the detailed phonon spectrum for Debye’s specific heat or the shape of the Fermi surface in the theory of not unders~d normal metals. If it had been necessary to do them this way, case by case, we would a solids. I have made here essentially 3 points: (a) (b) fc)
Conceptual Depth Qualitative Tests Computational Opacity. PTUAL
DEPTK
Here then are serious problems with the “antiferromagnetic spin fluctuation theory” as proposed initially by Moriya and followed up by Scalapino, Millis and Pines. Antiferromagnetism in most substances in which it occurs is a consequence of their being Mot&Hubbard insulators. The corresponding superexchange theory is a proiective perturbation theory in l/U, which is carried over to the metallic state by the “t - J” ~~sfo~ation.
This is incompatible with a probation
in positive powers of U, since J = i
unless
major resummations are carried out. More important, the projective character of the t - J H~iltonian enforces a local constmint-i.e., an infinite number of conservations-which implies rigorously one Lagrange multiplier for each constraint, i.e., a massless gauge field. That the result can be modeled by simple perturbation theory is a bold, but almost certainly incorrect, conjecture. It does not work in one dimension, the only case we can rigorously solve. I have shown that it does not work in two, but my solution is approximate and only applies in the limit w + 0. 1457
P. W. ANDERSON
1458
IVE TESTS, t The question is whether there are any simple, generic behaviors, and whether they are indicated by this theory. The answers are yes and no.
Let me first dispose of a large class of red herrings. As Mott explained to us in 1949 and 1956, metal insulator transitions are usually discontinuous, and this one is no exception; as beautifully shown by the laser-induced superconductivity experiments among others. (Also by Jim Allen’s photoemission results.) Underdoped materials are pathological: either inhomogeneous or beset with localized defects. It is a pity so much good experimental effort has been wasted on them, especially the neutron work. There are two, essentially, stable metallic phases: fully doped and overdoped metals (often separated by a phase transition, as Takagi and Batlogg showed). The latter is more Fermi liquid-like; the former is the optim~ly doped superconducting phase. These optimally doped phases are remarkably similar in their normal state behavior; e.g, Batlogg has shown that dp&iT at - 100’ does not vary (per plane) by more than - 20% for 4 of them and I have estimated a number of others and found agreement They all show: (a)
Linear T and o resistivity: 9 = max(;)
(b) (c)
&falIOT+ (Mean fme pathlCCCc. (Infrared transparencyEk)
(a)
Linear w Raman background.
The most striking plot is of 9~~7’~
for a wide variety of these materials. The correlation
coefficient is exactly zero with probability unity: normal state properties are m with T,, from material to material, A theory which attempts to explain Tc with the same physics as normal state resistivity, as the spin fluctuations do, must encounter skepticism. (They are not alone, of course: anyons, spin bags, bipolarons, etc., all have the same problem.) There is no natural “back-of-the-envelope” explanation for any of these regularities. A number of other observations are almost equally generic and/or anomalous . The photoemission spectra are the most striking, as explained in my talk at this conference: spin fluctuations do not address these anomalies. The anomalous relaxation (Tl and T2) results in NMR are carefully fitted; but simpler*power law tits from other theories are equally good in the normal state.
0
COMPUTATIONAL OPACITY..
Finally, let me say a few words about computational “opacity” (my synonym for “complexity”). Because of the great popularity of the computer, especially as a training tool to keep the young gainfully, if not usefully, occupied, it has become somehow a sign of virtue for a theoretical investigation to involve heavy use of the computer, either for computation or for simulation. Of course the computer can be useful, but not, I would argue, in the kind of problem-~lving investi~tion necessary to unravel high TC. The minute a cakulation disappears into the computer it has become unch~~b~ and unedible. Physicists have learned that experiments m be independently reproduced before belief sets in, but unfortunately computer work has not been held to the same standard. This is necessary especially in the kind of calculations involved here, where there is a large universe of parameters, no control on the theoretical approximations used, the input experiments have unknown validity and limits of error, and there is no way for a completely independent investigator making independent choices to verify the results. I would argue that a claimed “nparameter fit” to an experimental datum carries little weight. This is true especially when every curve on every substance must be ~de~endy calculated in detail. I do not feel that one is dealing here with deliberate fraud, as may be the case with W. S. Goddard’s calculations, but rather with optimism and self-deception. I do feel that in our misuse of the computer we condensed matter physicists are in danger of opening ourselves to problems of ethics which we have been happily free from in the past.
D-wave superconductivity
1459
I do not want to end on such a finger-pointing tone. High Tc has confronted our community with a set of anomalies which am forcing us to go through a Kuhnian (mini-) revolution in our thinking. We are in the “crisis” stage in which similar past communities have often exhibited irrational behavior. It is not irrational for some to propose impossible conjectures in such a crisis; what is perhaps blameworthy is for the audience to take them seriously without checking them against reality. POSTSCRIPT The import of the above is that the specific shape of the energy gap is not very relevant to the problems of the theory. Nonetheless it is an interesting question. I do not see how either the observation of an isotope effect in many cases or the insensitivity of Tc to massive amounts of dopant impurities can be made compatible with a gap with nodes, unless new physics is involved. My guess is an anisotropic s-wave gap. The data are not inconsistent with that calculated by Chakravarty et al. The claim that the impurity effect has been calculated in s.f. theory is nonsense, since the absence of residual resistance is not explained in that theory.